Relation of internal attenuation, dust emission, and the size of spiral galaxies. Calibration at low-z and how to use it as a cosmological test at high-z

Dust in spiral galaxies produces emission in the far-infrared (FIR) and internal absorption in visible wavelengths. However, the relation of the two amounts is not trivial because optical absorption may saturate, but the FIR emission does not. Moreover, the volume concentration of dust plays a role in the relation of absorption and emission, which depends on the size of the galaxy. We explore the relation of these three quantities. In order to understand the geometrical problem, we developed a model of dust distribution. We also investigated the relation of the three variables with real data of spiral galaxies at z<0.2 using the spectroscopic SDSS and FIR AKARI surveys. Internal absorptions were derived with two different methods: the ratio of emission lines H$_\alpha $ and H$_\beta $, and a previously calibrated relation based on the color variations as a function of absolute magnitude and concentration index. We find that in our low-z sample, the dependence of the average internal attenuation on galaxy size is negligible on average. It allows us to derive the internal attenuation of the galaxy, $A_V$, even when we only know its FIR flux. This attenuation approximately depends on the inclination of the galaxy $i$ as $\overline {A_V}=\gamma_V \log _{10}\left(\frac{1}{\cos i}\right)$, where $\gamma_V$ is a constant. We found that $\gamma_V$ has a maximum value of $1.45\pm 0.27$ magnitudes. When similar properties of dust are assumed, a general expression can be used at any $z$. For cases of nonsaturation, this might be used as a cosmological test. Although the present-day sensitivity of FIR or mm surveys does not allow us to carry out this cosmological test at z>2 within the standard model, it may be used in the future. For much lower z or different cosmological models, a test might be feasible at present.